Define and Use Zero and Negative Exponents February 24, 2014 Pages

1. 3 – 2 Definition of negative exponents 1 9 = Evaluate exponent. 2. (–7 ) 0 Definition of zero exponent = = 1 Evaluate the expression. **Hint: look at Key Concepts Pg = 25 Simplify by multiplying numerator and denominator by 25. = – Definition of negative exponents = Evaluate exponent.

4. 0 – 5 a – n is defined only for a nonzero number a (Undefined) = Definition of zero exponents = 1 Definition of negative exponents 1 64 = Evaluate exponent. 6. (–8) – 2 1 (–8) 2 = Definition of negative exponents –3 = 8 = 2 3

8. (–1 ) 0 Definition of zero exponent = – Product of a power property = 6 0 Add exponents. = 1 Definition of zero exponent = 6 – 4 + 4

1 256 = Evaluate power – 4 Definition of zero exponent Evaluate power. = 81 = 3 4 Power of a product property = 4 – 4 Multiply exponents. Definition of negative exponents 10. (4 – 2 ) = 4 2 = 4 – 2

1 125 = Evaluate power – Quotient of powers property = 5 – 3 Subtract exponents = Definition of negative exponents = 5 – 1 – – 3 Definition of negative exponent Evaluate power. = 64

Product of a power property = (– 3) 0 Add exponents. = 1 Definition of zero exponent = (– 3 ) 5 + ( – 5) 14. (– 3 ) (– 3 ) – 5 5 Evaluate power = – Quotient of powers property = 6 – 4 Subtract exponents = Definition of negative exponents = 6 – 2 – 2

Simplify the expression. Write your answer using only positive exponents. 16. (2xy – 5 ) 3 = 2 3 x 3 (y – 5 ) 3 = 8 x 3 y – 15 = y 15 8x38x3 Power of a product property Power of a power property Definition of negative exponents

y5y5 (2x) 2 (– 4x 2 y 2 ) = (2x) – 2 y 5 – 4x 2 y y5y5 4x 2 (– 4x 2 y 2 ) = y5y5 –16x 4 y 2 = y3y3 16x 4 – = Power of a product property Definition of negative exponents Product of powers property Quotient of powers property

3x3x (y 3 ) (9x 3 y) = 3xy – 3 9x3y9x3y Simplify the expression. Write your answer using only positive exponents. 9x3y9x3y 3xy – x2y43x2y4 = Power of a product property Definition of negative exponents Quotient of powers property 3x3x 9x 3 y 4 = 18.

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